{"id":"W2964292677","doi":"10.1142/s0219199710004019","title":"MINIMAX PROBABILITIES FOR AUBRY–MATHER PROBLEMS","year":2010,"lang":"en","type":"article","venue":"Communications in Contemporary Mathematics","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Minimax; Mathematics; Duality (order theory); Characterization (materials science); Mathematical economics; Discrete time and continuous time; Minimax theorem; Applied mathematics; Discrete mathematics; Statistics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.002073392,0.0003304362,0.0006517067,0.0002004836,0.0002151496,0.0001160545,0.001679908,0.0002531547,0.0001075596],"category_scores_gemma":[0.002983425,0.0002924844,0.0002070738,0.0002932157,0.0004358689,0.0002721569,0.0004164123,0.0005891257,0.00003393152],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004600978,"about_ca_system_score_gemma":0.0001661976,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001301567,"about_ca_topic_score_gemma":0.0002703943,"domain_scores_codex":[0.9976171,0.00009420294,0.001323696,0.0003215921,0.0002644633,0.0003789731],"domain_scores_gemma":[0.9909857,0.004848944,0.0004502549,0.003346978,0.000252869,0.0001152602],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000006593903,0.001402554,0.000234383,0.001052309,0.00003651881,6.65636e-7,0.003412352,8.603598e-7,0.0007671976,0.9903965,0.002131176,0.0005588871],"study_design_scores_gemma":[0.0006251422,0.00005466548,0.00002363747,0.000249675,0.0000230911,0.00001173348,0.0008523529,0.03525218,0.00009054402,0.9443706,0.01810211,0.0003442695],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2949331,0.001307049,0.1565576,0.01210811,0.0009391458,0.01699939,0.0004843731,0.001311419,0.5153598],"genre_scores_gemma":[0.5144807,0.00002752052,0.4815719,0.00006896066,0.0000395623,0.001328179,0.00003805935,0.00008666528,0.002358483],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5130013,"threshold_uncertainty_score":0.9999527,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.262573423244908,"score_gpt":0.4012187957585848,"score_spread":0.1386453725136768,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}